John Nelder, who has died aged 85, developed several fundamental approaches to data analysis that have been incorporated into key statistical software systems. Scientists in disciplines as diverse as genetics and geology, physics and pharmacology, chemistry and climatology, economics and evolutionary biology, make constant use of approaches based on his work.

John's first post, from 1949 to 1968, was at the National Vegetable Research Station at Wellesbourne, Warwickshire. There he built on the work of the statistician and evolutionary biologist Ronald Fisher, who had shown how the variation observed in yields and other measurements from agricultural experiments could be attributed to the effects of treatments such as fertilisers, and compared to random variation by using a technique that he called analysis of variance (Anova).

In complex experiments, it was not always easy to see how Anova should be applied. The analysis might need to allow for several types of random variation: there might be fertility trends up and down as well as across a field, or the experiment might have been run at several different times or locations. Types and amounts of fertiliser, types of crop and plot sizes might also vary.

So scientists relied on a repertoire of standard experimental designs, each with its own recipe for analysis. In two Royal Society papers published in 1965, John developed a general theory covering a wide class of designs, which suggested that they could all be analysed by a single algorithm, or computational method. The implication was that computer code could be written that would allow experimental data to be analysed according to key features. John then visited Adelaide, where he worked with Graham Wilkinson. As a result of their collaboration, the algorithm became an important part of a statistical program that laid the foundations for a system now known as GenStat for Windows.

In another 1965 paper, written with Roger Mead, John described a new approach to function optimisation, such as which settings of a combustion engine would minimise carbon monoxide output. The resulting Nelder-Mead simplex algorithm has become a standard tool for scientists in every discipline. In 1968, John became head of statistics at the Rothamsted agricultural research station, at Harpenden, Hertfordshire, where he developed GenStat as a general-purpose system providing a full suite of statistical facilities. John soon also began a collaboration with Robert Wedderburn, who died in 1975 at the age of 28.

Before their work, statisticians had had difficulty in analysing data where the random variation did not come from the familiar – bell-shaped – normal distribution. So data sets that consisted, for example, of counts of insect pests on plots treated in various ways received approximate analyses that could lead to erroneous conclusions. A 1972 paper by Nelder and Wedderburn showed how data from several popular non-normal distributions could be regarded as special cases of a general class that they called generalised linear models (GLMs). This theory again led to a single, powerful algorithm, which provided the basis for a further statistical package, GLIM, before being incorporated into GenStat and many other packages.

John was born at Brushford, on the edge of Exmoor. His father, grandfather and great-grandfather kept the Carnarvon Arms, where he grew up. Explorations of the nearby Exe and Barle rivers led to a lifelong love of nature. He met his future wife, Mary, whom he married in 1955, through birdwatching.

Educated at Blundell's school, in Tiverton, he went to Sidney Sussex College, Cambridge, where he studied maths. This was interrupted by second world war service, much of it in South Africa, as a navigator for the RAF. John graduated in 1948, and took the diploma in mathematical statistics. His enthusiasm for statistics carried over into his hobby of ornithology. He was proud of his paper in British Birds in 1962, pointing to the implausible number of rare bird sightings around Hastings in the early 1900s.

John retired from Rothamsted aged 60, but his statistical output continued undiminished. For the next 25 years his striking, tall and moustached figure was a familiar sight at Harpenden station, waiting to board the train to London and Imperial College, where he had a visiting professorship. He began a research partnership there with the Korean statistician Youngjo Lee and they extended the work on GLMs to include the analysis of more complex data sets, in which random variation was generated from several different sources. John was elected a fellow of the Royal Society in 1981, and won the Guy medal in silver and gold of the Royal Statistical Society, which he served as president (1985-86).

The annual musical matinees at his home, Cumberland Cottage, with entertainment provided by John, a brilliant pianist, and food by Mary, were a joy. He is survived by Mary and their children, Jan and Rosalind.

• John Ashworth Nelder, statistician, born 8 October 1924; died 7 August 2010